AI in biochemistry

Today we observe a pervasive presence of AI in tackling complex biochemical challenges, such as:

1. Predicting protein conformation
2. Predicting protein-protein interactions
3. Predicting protein-ligand interactions

However, the pace at which such AI systems have been developed has outstripped the development of explainable models or validations of their robustness.

Protein pocket detection

Protein pocket detection

GENEOnet

GENEOnet [1] is a specialized GENEO [2] network model designed for detecting protein pockets, it features a shallow architecture composed of a small number of GENEO units.

Notably, it is an explainable by design model, we compared its performances with other state-of-the-art methods finding that it has better results despite its greater simplicity.

GENEOs (informally)

GENEOnet was developed with GENEOs (Group Equivariant Non-Expansive Operators) which are mathematical tools that can be combined into network models featuring:

1. Coherence with respect to geometrical transformations of the data
2. Stability with respect to perturbations of the data

GENEOs

Fix two spaces of real valued functions \(\Phi\), \(\Psi\) and two groups \(G\), \(H\) of transformations of their domains.

Definition 1: (GENEOs) A map \(F \colon \Phi \to \Psi\) is called a Group Equivariant Non-Expansive Operator if, fixed \(T\colon G\to H\), the followings hold:

1. \(F(\varphi \circ g) = F(\varphi) \circ T (g)\) for every \(\varphi \in \Phi\), \(g \in G\) (equivariance)

2. \(||F(\varphi) - F(\varphi')||_{\infty} \le ||\varphi - \varphi'||_{\infty}\) for every \(\varphi, \varphi' \in \Phi\) (non-expansivity)

GENEOs

Fix two spaces of real valued functions \(\Phi\), \(\Psi\) and two groups \(G\), \(H\) of transformations of their domains.

Definition 1: (GENEOs) A map \(F \colon \Phi \to \Psi\) is called a Group Equivariant Non-Expansive Operator if, fixed \(T\colon G\to H\), the followings hold:

1. \(F(\varphi \circ g) = F(\varphi) \circ T (g)\) for every \(\varphi \in \Phi\), \(g \in G\) (equivariance)

2. \(||F(\varphi) - F(\varphi')||_{\infty} \le ||\varphi - \varphi'||_{\infty}\) for every \(\varphi, \varphi' \in \Phi\) (non-expansivity)

We retrieved MD simulations data from ATLAS [4] then:

1. We selected the first \(T\) frames for each protein \(P\).
2. For \(t=1,\dots,T\) we computed GENEOnet global prediction \(G(P_t)\) (i.e. the union of all predicted pockets).
3. For \(t=2,\dots,T\) we computed the Overlap and the RMSD between the current and the preceding frame: \[ \begin{aligned} O_t (P) &= \frac{|G(P_{t-1} ) \cap G(P_t )|}{ |G(P_{t-1} )|} \\ RMSD_t (P) &= \sqrt{\frac{1}{N} \sum_{j=1}^N||\mathbf{x}_{t-1}^j - \mathbf{x}_t^j ||^2} \end{aligned} \]

Evaluation

To assess GENEOnet’s robustness [5] [6] we compared the distributions of Overlaps and RMSDs for the 37 proteins considered expecting that:

1. Small values of RMSD should imply high values of Overlap.
2. High values of RMSD may imply small values of Overlap since it is possible that the larger movements between frames impact areas where no pockets are predicted thus having smaller effects on the Overlap.

Comparing the distributions

Boxplots of RMSD and Overlap

Takehome message

GENEOs can be used to develop explainable by design AI models which are also robust to perturbations in the data as shown with GENEOnet and MD simulations.

Extended work